Answer:
Part a) The area of the actual floor is [tex]576\ ft^{2}[/tex]
Part b) The ratio of the area in the drawing to the actual area is [tex]\frac{1}{16}\frac{cm^{2}}{ft^{2}}[/tex]
Step-by-step explanation:
step 1
Find the length of the square floor on a scale drawing
Let
b-----> the length side of the square floor on a scale drawing
we know that
[tex]A=b^{2}[/tex]
we have
[tex]A=36\ cm^{2}[/tex]
[tex]36=b^{2}[/tex]
[tex]b=6\ cm[/tex]
step 2
Find the length of the square floor in the actual floor
we know that
the scale drawing is [tex]1cm:4ft[/tex]
so
the length of the square floor in the actual floor is equal to
[tex]6*4=24\ ft[/tex]
step 3
Find the area of the actual floor
[tex]A=24^{2}=576\ ft^{2}[/tex]
step 4
Find the ratio of the area in the drawing to the actual area
[tex]\frac{36}{576}\frac{cm^{2}}{ft^{2}}[/tex]
simplify
[tex]\frac{1}{16}\frac{cm^{2}}{ft^{2}}[/tex]
